# On the distribution of the surplus prior to ruin

D. C M Dickson

Research output: Contribution to journalArticle

### Abstract

The distribution of the surplus immediately prior to ruin in the classical compound Poisson risk model was considered in a paper by Dufresne and Gerber (1988). The main purpose of this paper is to present a simple method for finding the distribution function and the density function of this surplus. We show that explicit solutions for these functions can be found when we know the probability and severity of ruin, denoted G(u, y). We also derive an algorithm which can be used to give approximate values of the distribution function when explicit solutions cannot be found. We also briefly consider the joint density of the surplus immediately prior to ruin and the deficit at the time of ruin. © 1992.

Original language English 191-207 17 Insurance: Mathematics and Economics 11 3 Published - Oct 1992

### Fingerprint

Explicit Solution
Immediately
Distribution Function
Compound Poisson
Density Function
Model

### Keywords

• Probability of ruin
• Recursive calculation
• Severity of ruin
• Surplus prior to ruin

### Cite this

Dickson, D. C M. / On the distribution of the surplus prior to ruin. In: Insurance: Mathematics and Economics. 1992 ; Vol. 11, No. 3. pp. 191-207.
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On the distribution of the surplus prior to ruin. / Dickson, D. C M.

In: Insurance: Mathematics and Economics, Vol. 11, No. 3, 10.1992, p. 191-207.

Research output: Contribution to journalArticle

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T1 - On the distribution of the surplus prior to ruin

AU - Dickson, D. C M

PY - 1992/10

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N2 - The distribution of the surplus immediately prior to ruin in the classical compound Poisson risk model was considered in a paper by Dufresne and Gerber (1988). The main purpose of this paper is to present a simple method for finding the distribution function and the density function of this surplus. We show that explicit solutions for these functions can be found when we know the probability and severity of ruin, denoted G(u, y). We also derive an algorithm which can be used to give approximate values of the distribution function when explicit solutions cannot be found. We also briefly consider the joint density of the surplus immediately prior to ruin and the deficit at the time of ruin. © 1992.

AB - The distribution of the surplus immediately prior to ruin in the classical compound Poisson risk model was considered in a paper by Dufresne and Gerber (1988). The main purpose of this paper is to present a simple method for finding the distribution function and the density function of this surplus. We show that explicit solutions for these functions can be found when we know the probability and severity of ruin, denoted G(u, y). We also derive an algorithm which can be used to give approximate values of the distribution function when explicit solutions cannot be found. We also briefly consider the joint density of the surplus immediately prior to ruin and the deficit at the time of ruin. © 1992.

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KW - Recursive calculation

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